Precipitation from Supersaturated Aluminate Solutions
II. Role of Temperature
H. A. V A N S T R A T E N AND P. L. D E B R U Y N
Van't Hoff Laboratory, Transitoriurn 3, Padualaan 8, 3584 CH Utrecht, The Netherlands
Received February 21, 1984; accepted May 15, 1984
The effect of temperature on the precipitation of aluminum hydroxide from dilute potassium
aluminate solutions (C~a<OH~,= 4 X 10-3 M) was studied in acid titration and pH-stat experiments.
The precipitation sequence is largely dictated by the supersaturation (II) and follows the Ostwald rule
of stages: amorphous --* pseudoboehmite --~ bayerite --~ gibbsite. The precipitation boundaries,
-log aAltOH~/aoH-,of the amorphous phase (-1.9) and pseudoboehmite (-1.2) evaluated by interpretations of relaxation time curves are temperature insensitive. The interpretation of relaxation curves
in the supersaturation region where pure bayerite forms is based on a surface nucleation mechanism
and allows estimates of the free energy of formation of the critical nucleus (~20 El/mole), interfacial
tension and two activation energies (-30 El/mole, +95 El/mole). The preferred formation of
pseudoboehmite at high pOH is shown to be the result of a lower interfacial energy and the retarding
effect it exerts at all temperatures on the competing growth of bayerite crystals. The growth rate of
bayerite is shown to be proportional to the available surface and the square of the supersaturation
and is characterized by an activation energy of about 60-80 El/mole. © 1984AcademicPress,Inc.
INTRODUCTION
In a previous publication (1) we reported
on the formation o f different a l u m i n u m hydroxide phases from supersaturated aluminate
solutions at r o o m temperature. U n d e r the
experimental conditions investigated, the observed precipitation sequence ( a m o r p h o u s pseudoboehmite-bayerite) was noted to conform to the so-called Ostwald rule o f stages
(2). F r o m a detailed analysis o f the relaxation
behavior o f the supersaturated solutions at
constant pH, it b e c a m e apparent that the
nucleation and growth o f the m o s t stable
solid phase (bayerite) was retarded by heterogeneous nucleation o f pseudoboehmite. Experiments c a r d e d out at different aluminate
concentrations and p H values revealed the
relaxation behavior to be determined mainly
by the degree o f supersaturation (II).
In this paper we report on the influence
o f temperature on the relaxation behavior o f
supersaturated aluminate solutions with an
initial aluminate concentration (CAI) o f 4
X 10 -3 M and an ionic strength o f 0.15 M
(KNO3). We are interested in the temperature
dependence o f the different processes which
were shown to be responsible for the relaxation behavior at r o o m temperature and the
evaluation o f the activation energy from such
measurements. Furthermore, as it is generally
reported (3-5) that the formation o f the m o s t
stable solid modification (gibbsite) from aluminate solutions is favored kinetically at
higher temperatures, we are also interested
in establishing h o w this phase modifies the
already complex precipitation behavior.
EXPERIMENTAL
T h e precipitation o f the solid phase from
supersaturated aluminate solutions in the
temperature range, 25 to 9 0 ° C was studied
by the same experimental techniques described in the earlier publication (l). Freshly
diluted stock solutions containing 4 X 10 -3
260
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All rights of reproduction in any form reserved.
Journal of Colloid and lnterfilce Science, VoL 102. No. 1. November 1984
PRECIPITATION FROM SUPERSATURATED ALUMINATE SOLUTIONS, II
M aluminate, an OH/AI ratio of 6.66 and of
total ionic strength 0.15 M (KNO3) were
titrated with an 0.25 M HNO3 solution in a
reaction vessel (final volume 3 liters) of special
design. All chemicals were of reagent grade,
freshly twice-distilled water was used and the
titration was performed under a nitrogen
atmosphere to eliminate CO2. The temperature during the titration and pH-stat experiments was controlled by means of a Lauda
NB-S 15 thermostat. Electrodes (Type Ingold
HA 465-35-90 with a double liquid junction)
were calibrated before and after each experiment at the measuring temperature with
standard Electrofact buffers (pH values 6.98
and 9.18 at 25°C). In the titration experiments the titrant was added at a constant
rate and pH of the solution was followed
with a Mettler pH-meter connected to a
recorder. In the pH-stat experiments, the
amount of acid needed to maintain a constant
pH was supplied by an automatic burette
and was registered by a recorder. Samples
taken from the reaction vessel were pressurefiltered through Millipore paper (0.65 ~tm),
washed with twice-distilled water and airdried at the temperature of preparation. The
solids were characterized by X-ray, IR, EM,
and BET adsorption techniques.
RESULTS
a. Titration Experiments
In our studies at 25°C (1) for relatively
fast titrations a characteristic pseudoequilibrium curve was obtained when plotting
pH or pH + pA1T (in the case of varying
total aluminate concentration, A1T) against
the ratio, OH/A1. In alkaline solutions the
temperature dependence of the pH at constant pressure (P) and amount of base (mKOH)
may be expressed by the relation
(dpKw]
= k ~ l P ,
(dpOH]
mKo H
-- ~
aJ---""7~JP,mKOH
[ 1]
261
where Kw is the dissociation constant of
water. When the concentration of hydroxyl
ions is large compared to that of hydrogen
ions, as would be true even for weakly alkaline solutions, Eq. [ 1] shows that
(d(pOH)~
~
l ~,m~o. TM 0
(dpKw~
dpH
There is a negligible temperature dependence
of the pOH of a solution at fixed amount of
added base, whereas the change in pH under
these conditions is determined largely by the
temperature coefficient of the water dissociation constant Kw. This analysis suggests that
a comparison of titration results at different
temperatures should be done preferably by
plotting pOH (rather than pH) versus OH/
AI. Such a plot is given in Fig. 1 for three
different temperatures (25, 50, and 60°C)
and the same constant titration speed of
0.024 mole acid mole -1 A1 min -1.
The titration curves may again be divided
into two regions. In region A essentially
neutralization of excess alkali occurs. We
also note that here Eq. [2] is well obeyed.
Precipitation takes place in region B. The
drop in pOH at 50 and 60°C (curves a and
b) implies that the rate of solid phase formation exceeds the titration speed. At 25°C
(curve c), for the same titration speed, a
2.
pOH 5
7.
-Region A
--Region B - -
FIG. 1. Titrationcurves (pOH vs OH/AI) at constant
acid addition rate (0.024 mole H+/(mole AI min)). (a)
60°C; (b) 50°C;(c) 25°C. Initialaluminateconcentration:
4 × 10-3 M, ionic strength0.15 M.
Journalof Colloidand InterfaceScience, VoL 102, No. 1, November 1984
VAN STRATEN AND DE BRUYN
262
pseudoequilibrium state is approached. This
kinetic behavior is clearly illustrated in Fig.
2 where the effect of different titration rates
on the kinetics of precipitation in region B
at a temperature of 50°C is presented. Only
at the highest acid addition rate (0.18 mole
acid mole -1 A1 m i n -l) the characteristic
pseudoequilibrium curve (see the titration
curve c at 25°C in Fig. 1) is registered.
Lowering the titration speed increases the
relative rate of solid phase formation and at
the lowest rate of acid addition (0.005 mole
acid mole -1 AI min -1) even a two-step process
(indicated by two dips in the titration curve)
becomes evident.
Solid state analysis of the precipitates
showed that at high titration rates an amorphous phase is formed (titration curve at
25°C in Fig. 1 and curve a in Fig. 2), whereas
on lowering the rate of acid addition
or increasing the temperature, increasing
amounts of pseudoboehmite precipitate (Fig.
1 and curves b and c in Fig. 2) formed. In
the titration experiment (curve d, Fig. 2)
small amounts of bayerite were also detected
and at the lowest titration speed (curve c,
Fig. 2) the increased amount of this crystalline
phase is evidenced by the second dip in the
curve. Small amounts of gibbsite were also
noted in the latter experiment.
In general it m a y be stated that the occurrence of a pseudoequilibrium titration curve
pOH
4-
5
4
a
OH~I--
FIG. 2. Titration curves at constant temperature(50°C)
for five different addition rates in mole H+/(mole AI
min). (a) 0.18; (b) 0.091; (c) 0.044; (d) 0.019; (e)0.005.
Initial aluminate concentration: 4 × 10-3 M, ionic
strength 0.15 M.
Journal of Colloid and Interface Science, Vol. 102, No. 1, N o v e m b e r 1984
2
I,
pOH
OH/AI -
-
FIG. 3. Theoretical equilibrium titration curves at
50°C for four different phases. Estimated solubility products (pK = -log(a^ltoHff/aoH-)): (a) Amorphous pK
= - 1.9. (b) Pseudoboehmite pK = - 1.1. (c) BayeritepK
= 0.3. (d) Gibbsite pK = 0.87. Three kinetic paths are
indicated resembling actual experiments (see Figs. 1
and 2).
is determined kinetically by the titration speed
and temperature. For example, at 25°C deviation from the (pseudo) equilibrium formation of an amorphous solid phase was
observed by Stol (6) to occur only at titration
speeds lower than 0.003 mole acid mole -1
A1 min -1. We have shown (1) that the pseudoequilibrium curve for the amorphous solid
phase at 25°C m a y be synthesized by assuming two fast equilibrium reactions
H + + OH- ~
H20
Kw (25°C)
= 10 -14
AI(OH)4 + H + ~ AI(OH)3 + H 2 0
K2 (25°C) -~ 8 × 10 -13.
Hypothetical equilibrium titration curves for
the formation of the other solid modifications
can be calculated in an analogous way if the
appropriate solubility product is known. In
Fig. 3 we present calculated equilibrium titration curves for the different AI(OH)3 solid
phases based on estimated values of the
solubility products at 50°C. Note that curve
d, the equilibrium curve for the formation
ofgibbsite, will only be obtained at extremely
low titration rates.
F r o m nucleation theory we know that a
critical supersaturation is needed for the formation of a significant n u m b e r of critical
nuclei after which growth of the new phase
m a y proceed at a rapid rate. This happening
PRECIPITATION FROM SUPERSATURATED ALUMINATE SOLUTIONS, II
will be detected in the titration curve as a
drop in the pOH value. Once a certain pOH
value is exceeded the growth process will be
faster than the acid addition. In Fig. 3 we
have sketched a few precipitation paths which
resemble the experimental titration curves
observed by Stol at room temperature (6)
and by us at higher temperatures. Path 1 will
be followed at high titration rates and will
coincide with the calculated curve for the
amorphous phase. Apparently this phase
forms at relatively low supersaturations as is
evidenced by the absence of a dip in the
titration curve over a 10-fold change in titration speed (1). Path 2 will be obtained at
intermediate titration rates where the drop
in pOH corresponds to rapid growth of pseudoboehmite once a certain pOH value is
reached. Path 3 will be followed when, in
succession, pseudoboehmite and bayerite
foo
263
1.o
a
lo
[
ot
ao
so
time (rain)
,.ot
I
o.5
o 2o
16o
time (min)
! 1.![
| o
b
260
~
e
./_
20
16o
260
time (rain)
wo i s, Alt ouot equ itative
interpretation of the experimental titration
curves is straightforward as illustrated by Fig.
3, a quantitative determination of solubility
products from such curves is hazardous.
b. pH-Stat Experiments
In these experiments our attention was
focussed on relaxation experiments at pOH
values in region A (Fig. 1) where immediate
formation of the amorphous phase could not
take place. From experiments conducted at
different temperatures and pOH values we
are able to distinguish four types of relaxation
curve. Representative examples of these types
are displayed in Fig. 4, based on experiments
performed at 50°C at different pOH values
and hence varying initial supersaturations.
The experiments were actually performed at
a constant pH but because of the water
dissociation equilibrium (7) this also implies
constant pOH. The ordinate axis in these
relaxation curves describes the normalized
uptake of acid, a(t)= A[H+(t)]/AIT where
A[H+(t)] is the cumulative uptake of acid at
time t and A1T is the total amount of aluminate.
T
ol •
I ol
J
i
20
loo
200
time (min)
FIG.4. Typesof relaxationcurves(a versus t) at 50°C.
Arrows locate time at which uptake rate is at its maximum. (a) pOH 4.35, (b) pOH 4.15, (c) pOH = 4.05, (d)
pOH = 3.75.
At a high pOH value (high supersaturation)
a regular S-shaped relaxation or acid uptake
curve is registered (Fig. 4a), it is replaced at
a slightly lower pOH (lower supersaturation)
by a curve characterized by two inflection
points (Fig. 4b), which in turn is succeeded
by a typical curve illustrated in Fig. 4c which
at the lowest pOH value again becomes Sshaped (Fig. 4d). At supersaturations higher
than those characteristic of Fig. 4a rapid
formation of an amorphous phase ensues, a
situation which we wished to avoid. The
same sequence of relaxation curves depicted
in Fig. 4 was also found at 75 and 90°C. At
25°C (1) the relaxation curves, types b, c,
and d, were also observed but not type a. At
this temperature type b curve persisted until
Journal of Colloid and Interface Science,
Vol. 102, No. 1, N o v e m b e r 1984
264
VAN STRATEN AND DE BRUYN
ation curves and X-ray and IR analyses. The
phase which is indicated in the lower part of
the composition block (rectangle) is in most
cases the first phase to form at that pOH and
temperature. We note that the sequence in
which the different phases precipitate is largely
determined by the pOH value. Especially at
75 and 90°C, large amounts of gibbsite are
seen to form at low pOH values. Remarkable
is the occurrence at 50°C of small amounts
of gibbsite at high pOH values where also
pseudoboehmite forms; it could not be detected at low pOH values where bayerite
predominantly forms. We also note that bayerite which is present in overwhelming
amounts at 25°C over a wide pOH range is
displaced kinetically by pseudoboehmite at
high pOH values and by gibbsite at low pOH
values, when the temperature is increased. It
should be realized, however, that this kinetic
precipitation diagram is representative for
relatively fast relaxation experiments (duration 1-10 hr) and that aging of the end
products in the mother liquor could involve
further phase transformations. Although this
effect was not investigated in detail an interesting result was obtained on aging pseudoboehmite samples at the ambient temperature
and pOH 4.35. At 50°C a substantial amount
of this solid modification was observed to
transform into bayerite over a period of a
few weeks (24 hr ~ 15%, 3 weeks --, 80%
transformation), however, at 75°C pseudoboehmite was still present in large amounts
after an aging period of 4 weeks. This kinetic
phenomenon may be correlated with the
results of Chang (8) who concluded from an
analysis of the thermodynamic data that the
transition temperature between gibbsite and
boehmite is 60 + 3°C with the former phase
more stable below this temperature. Above
this temperature it is then more likely
that pseudoboehmite transform directly into
'q
pOH boehmite.
FIG. 5. Histogram of the solid phases formed as a
A characteristic difference between pseufunction of temperature and pOH. The lower parts of
doboehmite
and bayerite is the much higher
the diagramsrepresent in general the first phase which
specific
surface
of the former compared to
is formed.[] Amorphous.[] Pseudoboehmite.[] Bayerite.
I~ Gibbsite
the latter. In Fig. 6 the BET specific surfaces
the precipitation boundary for the amorphous
phase was reached, then a three-step curve
appeared where the fast initial uptake of acid
(formation of amorphous phase) is followed
by a curve similar to type b in Fig. 4. The
four types of relaxation curve (Fig. 4) are
closely connected with changes in the nature
of the precipitating solid phases. At high
supersaturations (Fig. 4a) only pseudoboehmite was observed to form, at somewhat
lower supersaturations (Fig. 4b) pseudoboehmite formed initially and in the second
stage (beyond the second inflection point)
mainly bayerite formed. At low supersaturations (Fig. 4d) almost exclusively bayerite
formed except that at higher temperatures
(75-90°C) noticeable amounts of gibbsite
were also seen. The formation of gibbsite
was, however, never indicated by an inflection
point in the relaxation curve, in sharp contrast
to the appearance of bayerite after pseudoboehmite (Fig. 4b).
In Fig. 5 we give a schematic presentation
of the type of solid phases present in the end
product of the relaxation experiments (a(end)
- 0,8 + 0.1 for most experiments) as a
function of pOH and temperature. A rough
estimate of the relative amounts of the various
solid modifications is also included in Fig. 5.
The information displayed is based on relax-
Journal of Colloid and Interface Science, Vol. 102, No. 1, November 1984
30o
PRECIPITATION FROM S U P E R S A T U R A T E D A L U M I N A T E SOLUTIONS, II
~-~.--C~.,.~;f~
.a,(~=.2
265
phases during precipitation of supersaturated
aluminate solutions. It was possible to deduce
the precipitation sequence
amorphous --~ pseudoboehmite --~
200Specific
Surface
6[~_
4
100-
3.8
4.5
'=
4
3.3
3.5
pOH
FiG. 6. Specific surface area (m2/g) as a function of
pOH at 50 and at 75°C. The inserted figure is an
enlargement of the values between pOH 3.5 and pOH
4.3; (e) 50°C; (×) 75°C.
of the end product of relaxation experiments
is plotted against pOH at two temperatures
(50 and 75°C). We note that pseudoboehmite
has a specific surface area of about 250 m2/
g whereas the specific surface area of bayerite
(or gibbsite) is approximately lower by 2
decades. The sharp drop in the BET surface
area around a pOH value of 4.1 is connected
with the transition region between pseudoboehmite and bayerite. A similar conclusion
was drawn from measurements at 25°C (1).
In Fig. 7 some typical electronmicrographs
are given of the final products obtained in
the pseudoboehmite-region and in the bayerite-region. Although at first glance the bayerite particles appear to be somewhat irregular
in shape, they clearly show a tendency to
grow with a conical form. A similar observation was made by Violante and Violante
(23). Figure 7c illustrates practically all the
particles to exhibit a hill-and-valley structure
that is indicative of growth initiated by the
formation of two-dimensional nuclei. The
irregular nature of the growth ends suggests
that nucleation and outgrowth of these nuclei
is a continuous and simultaneous process.
bayerite ~ gibbsite
from experiments in which the aluminate
solution was apparently supersaturated with
respect to all of these solid modifications.
This sequence is seen to be in accord with
the Ostwald rule of stages which predicts that
the thermodynamically least-stable phase
should form first. Of fundamental interest to
the understanding of this complex precipitation system would be an evaluation of the
nucleation and growth characteristics of each
of the four phases. To accomplish this objective conditions must be established under
which the formation of a given solid phase
may be followed kinetically without interference by other precipitating phases.
The titration experiments indicated that
an amorphous phase is formed immediately
once a certain value of the supersaturation
(pAl - pOH ~< -1.9) is reached and the
titration speed lies above a limiting value. It
is, however, clear that the kinetics of formation of this phase would require measurement
of times in the (milli-) second range. This
requirement could not be met by our experimental approach. The titration experiments
at relatively low titration rates and the pHstat experiments did enable us to study the
kinetics of precipitation of the other three
solid phases. In addition we were able to
arrange the experimental conditions so that
it was possible to observe the separate formation of bayerite and pseudoboehmite. It
was not possible to establish precipitation
conditions where gibbsite may be said to
form without interference of bayerite. This
failure would seem to imply that the kinetics
of the formation of these two crystalline
phases is not significantly different.
DISCUSSION
Relaxation Behavior of the
Precipitating System
Titration and pH-stat experiments revealed
the possible formation of four distinct solid
Quantitative information about the nucleation kinetics may be extracted from the
Journal of Colloid and Interface Science, Vol. 102, No. 1, November 1984
266
VAN STRATEN AND DE BRUYN
FIG. 7. Electronmicrographsof samples obtained in experimentswhere mainly pseudoboehmite(a) and
bayerite (b) and (c) are formed. (c) the typical hill-and-valleystructures observed with bayerite particles.
(a) Pseudoboehmite,50°C, pOH 4.35; (b/c) bayerite, 50°C, pOH 3.55.
relaxation (pH-stat) experiments by introducing a relaxation time, tr (1). This parameter is defined as the time at which the
uptake-rate of acid (da/dt) reaches a maxim u m (see Fig. 4).
Figure 8 gives a plot o f the relaxation time
(tr) as a function of pOH at three different
temperatures. At 25°C, the relaxation times
at all pOH values refer to the times for
maximum rate of uptake o f acid in the
Journal of Colloid and Interface Science, Vol. 102, No. 1, November 1984
formation of bayerite. Only the right-hand
branch of this curve (pOH ~< 3.85) describes
the relaxations in which pure bayerite forms
(1). At 50 and 75°C it was possible to separate
in time the formation of bayerite and pseudoboehmite. At pOH values higher than that
indicated by arrow A (see Fig. 8) the relaxation times refer to the formation of pure
pseudoboehmite and at pOH values lower
than that indicated by arrow B the relaxation
PRECIPITATION FROM SUPERSATURATED ALUMINATE SOLUTIONS, II
ooo
J:ool
7
60
l
s°e
i
4'.5 .i
4.0
I ) O H - -
315
FIG. 8. Relaxation times (tr) as a function of pOH at
25, 50, and 75°C. At 25°C the tr-values in the left-hand
branch refer to bayerite in the presence of (considerable)
amounts of pseudoboehmite.
times describe the formation of pure bayerite.
The relaxation times which determine the
behavior of the curves in the region between
arrows A and B refer to the formation of
bayerite under conditions where both phases
are known to be present. The same general
shape of the relaxation curves is seen to
characterize the precipitation at all three
temperatures except that the height of the
maximum in the curve is significantly reduced
at 50 and 75°C. We conclude from Fig. 8
that the same type of kinetic processes are
operable at the different experimental temperatures. At low pOH values a regular decrease in tr is measured for the bayerite (or
gibbsite) phase. In the region where small
amounts of pseudoboehmite form the relaxation time increases with increasing pOH
and at high pOH values where pseudoboehmite is a major (or sole) constituent a
smooth decrease in tr is again measured. We
have argued previously (1) that the minimum
in the curve at higher pOH values (at 25°C)
is due to the fact that heterogeneous formation of small amounts of pseudoboehmite on
bayerite particles retards further growth of
267
bayerite. This explanation remains valid at
higher temperatures except that the retardation effect is less pronounced. The observed
maxima at these higher temperatures are
clearly due to the increased rate of nucleation
of pseudoboehmite with increasing pOH as
expressed by the drop in tr. At 25°C this
decrease in relaxation time at high pOH
values is also observed but under these conditions the formation of bayerite and of
pseudoboehmite are not always clearly separated in time. The formation of both phases
must be accelerated by increasing pOH in
this pOH range, although the formation of
one phase may be relatively enhanced compared to the other.
The pOH of a supersaturated solution is
not a satisfactory measure of the degree of
supersaturation when one wishes to compare
precipitations at different temperatures. The
most general expression for the supersaturation II; of the aluminate solution with respect
to solid phase i is
pIIi= pAl - pOH - pKsp,i(T)
[3]
where the solubility product Ksp, i is defined
by
g s p , i - aAl(OH)i
[4]
aoH-
and pAl = -log aA~(on~.
As the solubility product is a function of
temperature we note from Eq. [3] that only
at a fixed temperature will changes in pII,- be
independent of the nature of the solid phase
which forms, and can pOH be used as a
useful relative measure of the supersaturation.
Unfortunately, except for gibbsite, the temperature dependent solubility products of the
various solid phases are not accurately known.
In Fig. 9 we have plotted log tr versus log ×
II~bbsite. The supersaturations with respect to
gibbsite were calculated from published data
by different investigators (9-12). The results
of some experiments at 62.5 and 90°C are
also included in this figure.
The displacement of the relaxation curves
at different temperatures is due to the strong
increase in the solubility of gibbsite with
Journal of Colloid and Interface Science, Vol. 102, No. 1, November 1984
268
V A N S T R A T E N A N D DE B R U Y N
Gibbsite
25 °
50o
~ - - kOgnGibbsi~e
FIG. 9. Log t, (min) versus the supersaturation (log
× H~b~) with respect to gibbsitc at 25, 50, 62.5, 75, and
90°C. (O) baycfitc at 25, 50, and 75°C. ([~) baycfitc at
62.5°C, (&) baycritc at 90°C, (×) baycrite at 25°C in
presence of substantial amounts of pscudobochmitc, (©)
pseudobochmite at 50, 75, and 90°C.
ture dependence of the solubility product of
pseudoboehmite may be estimated. It appears
then that the solubility product of pseudoboehmite is relatively insensitive to changes
in temperature over the range of temperatures
employed in this study. We estimate -1.2
> pKsp > -1.3 although this estimate may
be somewhat on the low side because even
for heterogeneous nucleation a slight supersaturation is needed. Based on the above
estimate the supersaturation with respect to
pseudoboehmite is found to be related to the
pOH by the expression, pOH ~ 3.7
-- plIpseudoboehmite.
The graphs in Fig. 8 may
thus also be interpreted as depicting the
change in tr with a change in the supersaturation with respect to pseudoboehmite.
Nucleation in Single (Solid) Phase Domains
increasing temperature. The two branches of
the relaxation curves corresponding to pure
bayerite and pure pseudoboehmite formation
are clearly defined in this logarithmic plot.
We have previously shown (see, for example,
Fig. 5) that replacement ofbayerite by gibbsite
at higher temperatures in the precipitation
sequence occurs without any detectable
change in shape of the relaxation curve (a vs
t). This observation considered together with
the similarity in the structure of these two
crystalline modifications suggest that the
temperature dependence of the solubility of
bayerite is of the same order of magnitude
as that of gibbsite. Hence the same shift in
the relaxation curves depicted in Fig. 9 would
occur if instead of log ]'Igibbsite, log IIbayerite
were to be plotted against log tr. We may
then conclude that at a fixed value of supersaturation the relaxation times for bayerite
will decrease with increasing temperature.
We have seen that the lowering of the
relaxation time of bayerite with increasing
supersaturation (or pOH) at a fixed temperature is arrested by the heterogeneous nudeation of pseudoboehmite. If it is assumed
that the composition of the solution at which
this retardation effect becomes just detectible,
corresponds to the precipitation boundary
(pI/ = 0) for pseudoboehmite, the temperaJournal of Colloid and InterfaceScience, Vol. 102, No. 1, November 1984
Under conditions where only one solid
phase is precipitating, the experimental relaxation time curves may be analyzed by application of classical nucleation theory (13).
According to this theory we may write
tr = r~(T) exp(AGJkT)
= r0 exp[(E(a[~ + AGc)/kT]
[5]
where r0 is some reciprocal frequency factor
and independent of temperature, ~(~)
~,act is an
apparent activation energy for the various
transport processes involved in the nucleation
step, and AGe is the free energy of formation
of a critical nucleus.
In the case of three-dimensional (3]:)) nucleation we write
A1;2cr 3
AG¢(3D) - (kT)2(ln ii)2
[6]
and if a two-dimensional nucleation step is
rate-determining
B134/3o-2
AGc(2D) = kT In II
[7]
In these expressions cr is the interfacial tension, v the mean ionic volume of the solid
phase, k the Boltzmann constant, and A and
B are constants determined by the geometrical
PRECIPITATION FROM SUPERSATURATED ALUMINATE SOLUTIONS, II
shape of the critical nucleus. In writing Eq.
[7] we have assumed a linear relation between
the edge free energy (or line tension) o and
the interfacial tension,
~r = p v -~/3.
[8]
269
its appearance. From these plots one may
then calculate z0, AGe, and a. We believe
that attempts to derive absolute values of the
interfacial tension are not only unwarranted
but would be misleading. However, when
different solids are compared or one solid
under different conditions, for example, at
different temperatures, changes in a, or some
relative measure of a, may provide useful
indications of certain trends.
As can be seen from Eqs. [6] and [7] in
order to evaluate a from plots such as shown
in Fig, l0 the molecular volume v, the shape
factor, and some relation between a and p
must be known. These parameters are not
accurately known, certainly not for particles
of the size of a critical nucleus. We avoid
this difficulty by defining an operational "interfacial tension,"
The relatively fast formation of pseudoboehmite and especially the high specific
surface area ( ~ 250 mZ/g) of this phase serve,
in our view, as indications that three-dimensional homogeneous nucleation is rate-determining for the overall precipitation process.
On the other hand, the slow (order of hours)
formation of the crystalline phase bayerite,
the low specific surface (.~ 1 to 5 m2/g), and
the hill-and-valley structure o f the growing
particles as seen under the electronmicroscope
(Fig. 7) suggest that a two-dimensional (surface) nucleation step is rate-determining for
the formation of bayerite.
tr* = (k/~f-B)T./~1/2
for 2D nucleation
An analysis o f the experimental results on
the basis of the above discussion is presented
= (k/A1/3)T . ~1/3 for 3D nucleation [9]
in Fig. 10 where we give a plot of In tr versus
where 3 and ~ are the respective slopes of
(In II) -2 for pseudoboehmite and of In t~
the plots o f In tr vs (ln 11)-1 and In tr vs
versus (In 11)-~ for bayerite, both at 50°C. A
(ln 1I) -2 (see Fig. 10). From Eq. [9] we then
straight-line behavior is noted in both plots
deduce that
over a supersaturation range where no inter~* = ~" v 2/~.
[10]
ference by the other phase is known to occur.
The two arrows in the figure locate the In order to derive values for ~* and In
supersaturation values at which the second × rb(T) the solubility products (Ksv) of the
phase (pseudoboehmite or bayerite) makes various phases must be known. A value of
0.7 has been estimated at 25°C (9, 12) for
pKsp(bay) = -log(aAl(On~/aom). To evaluate
pK~p(bay) at higher temperatures we assume
this phase to have the same temperature
6Bayerlte
l
dependence as gibbsite (9-11). This means
(0,3)
Intr
that A H ° for the reaction Al(OH)4(aq)
AI(OH)3(s) + OH-(aq) must be approxJmately
the same for bayerite and gibbsite--a reasonable assumption. For pseudoboehmite we
~ h m R e
choose pK~p = -1.1 a value that is slightly
higher than that estimated from an analysis
of the data in Fig. 9.
The calculated values of In rb(T), a* and
0'.1 013 015 0'.7
some
typical values o f AGe at four different
--0.,)-lo,0,n~
2
.
temperatures
are listed in Table I. It can be
FIG. 10. Plots of In tr versus 1/ln II for bayerite at
seen
that
both
a* and AGe decrease with
50°C and versus l/(ln II)2 for pseudoboehmiteat 50°C.
temperature
and
are higher than the pseuValues between parenthesis refer to the chosen solubility
product (pH = -log a~a(on~]aon-)for the solid phase.
doboehmite. If we were to assume that two-
t
Journal of Colloid and Interface Science, VoL 102, No. 1, November 1984
270
VAN STRATEN AND DE BRUYN
TABLE I
Parameters Describing Kinetics of Nucleation and Growth in Aluminate Systems
Temp.
(*C)
Phase
pK~
In T~T)
25 a
25
50
62.5
75
50
75
Bay
Bay
Bay
Bay
Bay
ps-B
ps-B
0.7
0.7
0.3
0.1
-0.05
-1.1
-1.1
- 2 . 3 + 1.3
36
_+ 6
7.4
-1
-3.3
-0.2
+0.9
-0.8
19
22
11.5
4.2
5.1
+ 1
± 8
_ 0.3
+ 0.3
_+ 0.9
5.9
6.5
4.9
1.35
1.6
± 0.4
+ 2.9
_+ 0.3
_+ 0.2
_+ 0.5
/3 or a
(Eq. [9])
a*
AGe
(kJ mole-I)
p
(H +)
_+ 0.6
21.2 ± 3.5
2.2 ± 0.1
±
±
_
+
+
15.5
21.7
13.4
4.0
5.2
2.4 ± 0.3
(ld mole-t)
0.1
1.1
0.1
0.05
0.1
+
_
±
±
+
0.8
8
0.4
0.3
0.9
2.4 ± 0.1
2.6 ± 0.2
3.5 ± 0.2
m
(AI)
2.0 + 0.1
1.9 ± 0.2
2.05 + 0.05
2.0___ 0.1
1.9 ± 0.1
0.8 b + 0.1
1 b + 0.1
n
(H +)
1.4 ± 0.3
1.7 ± 0.4
2.25 + 0.2
2.4 ± 0.2
2 ± 0.2
3.4 _ 0.2
Note. AGe is calculated at pOH 3.65 for bayerite and at pOH 4.35 for pseudoboehmite; for the calculation of a*
we assumed the shape factors to be, respectively, B = 4 (square) and A = 32 (cubic). ~tml) = - 3 0 _+ 10 kJ mole-l;
Eal
act = 95 + 10 kJ mole-l; E ~ = 60-80 kJ mole -l.
a pAlT = 1.8 otherwise pAIT = 2.4.
0 Order in (c^1 - cm,e).
dimensional nucleation is also rate-determining for the formation of pseudoboehmite the
calculated a* values for this phase would be
approximately higher by a factor two but still
less than those for bayerite. The determination of In r'o(T) is less accurate because of
the long extrapolation required (see Fig. 10).
In principle we can calculate the activation
energy E(~ (see Eq. [5]) from Arrhenius plots
of In r~ vs 1/T. On taking into account the
inaccuracies in evaluating In r~ we find for
bayerite formation an activation energy of
-30 _+ 10 kJ/mole.
It should be realized that absolute values
of a*, In r'o(T) and ~act17'(will
1) depend on the
chosen values of the solubility product. Calculations show, however, that on allowing
for an uncertainty in the pKsp values at 25°C
of as high as +0.4 units, would not alter the
indicated trends (Table I) in a* and the low
value of the activation energy.
The negative *-,acta~7(l)needs further comment.
The inaccuracy of the method used for evaluating the activation energy from relaxation
times must be considered in any interpretation of the observed negative value. We note,
however, that ~actW0)has been defined as an
effective activation energy for a combination
of elementary steps. A negative value may
therefore indicate that certain steps in the
nucleation process proceed faster at lower
Journal of Colloid and Interface Science, "Col.102, No. 1, November1984
temperatures. It has been argued that extensive hydrogen bonding exists in aluminate
solutions at low temperatures (14, 15). The
observed breakdown of structure at increasing
temperature is suggested to be complete at
75°C (16). Misra and White (17) suggested
that hydrogen bonding promotes nucleation
at low temperatures and to be ineffective as
a promotor above 75°C. This role of hydrogen bonding may be offered as a possible
(qualitative) explanation of the negative value
Ox¢ ~L,( 1act.
)
As mentioned earlier the determination of
absolute values of interfacial tension from
relaxation studies is not reliable. In conclusion
we nevertheless wish to quote an order of
magnitude estimate of the interfacial tension
(a) for bayerite and pseudoboehmite at 50°C.
For bayerite this estimate, based on a square
nucleus, a density of 2.5 g/cm 3 and a pKsp
of 0.7 + 0.3, is found to equal 67 + 20 toNI
m. For pseudoboehmite a value of about 25
mN/m is estimated. Considering the various
assumptions and inaccuracies involved in
making these order of magnitude estimates
the results are not unreasonable.
Activation Energies in the Nucleation of
Pure Bayerite
We note with reference to Fig. 9 that the
experimental results in the supersaturation
PRECIPITATION
FROM
SUPERSATURATED
region where essentially pure single phases
are being formed, may also be approximated
by the empirical relation ~
t~ = q,(T)II-C
[11]
The value of the exponent p at different
temperatures is obtained from the slope of
the curves at Fig. 9 and is listed in Table I.
We may also define an activation energy
E(2)
act which may be obtained from the ternperature dependence of ~,
E(,~ _ d In O(T)
R
d(1/T)
[131
d l n t~
d l n t~ (Eq. [111)
d In II (Eq. [5]) =
d In II
= -P"
[141
On making use of these conditions and Eq.
[7], it is readily shown that
E(1) 2AGe'M
In ~(T) = In ro + - - act
~ + kT
SOLUTIONS,
II
271
H-interval. From the values o f AGe listed in
Table I and the estimated value u~A"~,ct~(1)( - 3 0
k J/mole) we note that the last term on the
right-hand side of Eq. [16] makes by far the
greatest contribution to the apparent activation energy E~{ (=95 M/mole).
An alternative formulation of Eq. [16]
may be derived. According to classical twodimensional nucleation theory
nc
=
AGe
kTln II
[17]
[121 in which nc is formally the size of the critical
A value of 95 + 10 kJ/mole is calculated for
E(2)
in the temperature range, 25 ~< T
act
75°C, from an analysis of the plots in Fig.
9. This calculated value is positive and much
larger than that derived for ~act~°)( - 3 0 _+ 10
M/mole).
The relation between these two activation
energies may be derived in the following
manner. Assuming the validity of the classical
nucleation expression, Eq. [5], the following
two conditions must be satisfied in the middle
of the U-interval where the approximation,
Eq. [ 11 ], is valid:
t~ (Eq. [5]) = t~ (Eq. [11])
ALUMINATE
[15]
and
E(2)
= ~(1)
+ 2AGcM + 2 d(AGc,M) [16]
act
x-~ act
nucleus. In view of Eq. [14] this expression
also determines the exponent p (see Eq. [ 11 ]).
On introducing Eq. [17] in Eq. [15] we
obtain the desired alternative expression for
E(2)
act
E(2)
act
/ ~(1)
~ a c t -t-
2 [din II~
+ 2 In I I ( ~ ) M .
[18]
In the experiments the initial aluminate concentration was the same at all temperatures,
from Fig. 8 we note that the middle of the
H-interval lies at approximately the same
pOH value, and from Table I we observe
small changes in p with temperature. Equation [18], may therefore be written in a
simplified form
E(~{
r")
2 g [d In Kso~
= --F(1)aCt+ 2pAH °.
[19]
With A H ° ~ +30 kJ/mole (11) and 2 < p
< 2.5 we see that the apparent activation
energy E ~ ) is largely determined by the standard enthalpy of the precipitation reaction.
T d(1/T)
where the subscript M indicates that AG~(T)
is evaluated at the middle of the appropriate
Nucleation of Pseudoboehmite
The observation that at high temperatures
pure
pseudoboehmite may be grown under
'Nielsen (18) proposed a similar expression for the
conditions
(low pOH) where the supersatu(homogeneous) nucleation rate (~tr') over a limited
supersaturation region.
ration with respect to bayerite is expected to
Journal of Colloid and Interface Science, Vol. 102, No. 1, November 1984
272
V A N S T R A T E N A N D DE B R U Y N
be higher than that with respect to pseudoboehmite, needs further comment. This experimental fact is, of course, in agreement
with the thermodynamic interpretation of
the Ostwald rule of stages, however, in view
of the available kinetic information, this explanation is too simplistic and in fact unsatisfactory. With reference to Fig. 8 the lefthand branch (decreasing tr with increasing
pOH) of the relaxation curve at 50°C may
be assumed to relate to the nucleation rate
(inverse of tr) dependence of pseudoboehmite
on supersaturation (pOH). The absence of
detectible amounts of bayerite in the precipitate may then be cited as evidence that
under these conditions the rate of nucleation
of bayerite must be much smaller than that
of pseudoboehmite, and that the kinetic interpretation of the rule of stages is applicable.
These conclusions may now be validated by
extrapolating the right-hand branch of the
relaxation curve which describes the nucleation-rate dependence of pure bayerite (1)
into the pseudoboehmite-formation field. This
extrapolation may be done with the aid of
Fig. 10. By following this procedure we estimate that the relaxation times of pure bayerite
in the pOH range in which pseudoboehmite
forms are approximately equal to or slightly
higher than the experimental tr values. The
uncertainty in the exact value of the solubility
product of bayerite has been allowed for in
making this estimate. We must therefore
conclude that since the nucleation rate of
pure bayerite under these conditions (high
pOH) is not much different from that of pure
pseudoboehmite, the formation of bayerite is
effectively blocked (or retarded) by the presence of pseudoboehmite. This conclusion is
not surprising as we have previously seen
that the relaxation behavior of the system in
the region where mixed precipitates are present, must be due to retardation of bayerite
growth by the presence of small amounts of
pseudoboehmite. Our analysis of the lefthand branch of the relaxation time curve
may then be summarized by writing
Jexp
0
Jpsboehm
>~> OJ~bay
Journal of Colloid and Interface Science,
VoL 102, No. I, November 1984
where ~ is the nucleation rate of pure phase
i and 0 is a blocking factor which may vary
between 0 and 1 and which is approximately
zero in this case. This extrapolation when
applied at 75°C shows that at the highest
pOH-values the relaxation time is about 3
times smaller than for bayerite. At 75°C it is
therefore not necessary to introduce a blocking factor.
We noted earlier in the discussion of Fig.
5 that gibbsite is able to form at high pOH
values under circumstances where pseudoboehmite developed first. This precipitation
sequence may be accounted for by assuming
that the pseudoboehmite with its high specific
surface provides template material onto which
other phases may be formed heterogeneously.
Formation of gibbsite and not bayerite, becomes possible if the initial precipitation of
pseudoboehmite causes a substantial lowering
of the supersaturation to reach a value where
heterogeneous formation of the former phase
is favored.
Growth Rates of Solid Phases
As a starting expression for the phenomenological description of the rate of growth,
1~ = da/dt, of a solid from a supersaturated
solution we may write
1~ = k ( T ) . A .f(II)
[20]
where k ( T ) is an overall (heterogeneous)
reaction rate constant, A is the available
surface area, and f(II) is some function of
the supersaturation I-I. If we approximate the
function f(II) by a power function then
1~ = k ' ( T ) . A .IIm.
[21]
This approximation may be justified on the
basis of a detailed analysis of our experimental
growth curves but also on the theoretical
grounds. It has been shown that over limited
supersaturation ranges fundamental expressions of the growth rate based on various
physical models, agree with a power function
dependence on supersaturation. Spiral growth
models (19) describing crystal growth at very
low supersaturations predict a first order or
273
PRECIPITATION FROM S U P E R S A T U R A T E D A L U M I N A T E SOLUTIONS, II
second order dependence on the supersaturation. Surface nucleation growth models (20)
can give rise to high powers of m, especially
at low II and large interfacial tension. At
high supersaturations where the growth rate
may be diffusion-controlled m equals unity.
The temperature dependence of the reaction rate constant in Eq. [21] may be expressed by the Arrhenius relation
k'(T) = ko e x p ( - E ~ R T )
[221
where ~'t~
a-,act is an overall activation energy for
growth and includes the contribution of the
various elementary steps such as volume
diffusion, diffusion through a surface layer,
adsorption and dehydration of the growth
unit in a kink site.
The available surface for growth may be
approximated by the relation
A(t) = qa(t) 2/3
[231
with q a proportionality factor. This expression will hold if, once growth has started, no
new nuclei are generated and the shape of
the particles does not change during growth.
In the ideal case that N spherical nuclei are
present initially (t = 0),
3A1TMAI
q= \
[24]
• N 1/3
PAl
]
where A1T is the total amount of aluminate
in the system, and MAI and PAl, respectively,
the molecular weight, and density of the solid
phase, aluminum hydroxide.
On substituting Eqs. [22] and [23] into
Eq. [21] and introducing the definition of
the degree of supersaturation (Eq. [3]), we
find the expression for the growth rate
da(t)
dt
- ko e x p ( - E ~ R T ) ,
qa2/3(t)
×
= klot2/3(t)[1
where
-
or(t)] m
[H+]"[1
-
or(t)] m
Ks"~
[25]
k, = ko exp(-E~)t/RT)q[H+I"K~ m l
= k2[H+]"
[26]
J
and K w is the solubility product of the growing phase. The exponents m and n in Eqs.
[25] and [26] may not be equal, as both q
and/Co will depend on the pH of the growth
experiment. Certainly, the number N of
nuclei may change with pH and therefore
also q.
As pointed out previously (1), the reaction
order m with respect to the aluminate concentration may be evaluated by plotting the
function log[or(t)-2/3. da(t)/dt] versus log(1
a(t)) at a fixed temperature and at different
pH (pOH) values. Examples of such plots for
gibbsite, bayerite and pseudoboehmite the
dominant growth phase are given in Fig. 1 I.
For pure gibbsite and bayerite systems these
graphs show a straight-line behavior over a
wide range of aluminate concentration. When
substantial amounts of a second solid phase
are indicated during the growth period, deviation from this linear behavior is noted.
It should be noted that similar plots with
pseudoboehmite as the growth phase do not
yield straight lines. The linear behavior for
pseudoboehmite (illustrated in Fig. 11) is
obtained when -log[1 - a*(t)] instead of
-log[ 1 - a(t)] is plotted on the x-axis where
a*(t) = A[H+(t)]/(A1T - A l E ) and AlE, the
equilibrium aluminate concentration, is evaluated by assuming pKsp (pseudoboehmite)
= - 1.1. The growth rate of pseudoboehmite
is therefore shown to depend on the concentration difference, Cgl(t) -- C~a(equil).
The exponent n (or the reaction order with
respect to the hydrogen ion concentration)
may be determined next by plotting log kl,
the intercept on the ordinate axis (Fig. 11),
against pH at a fixed temperature. This plot
also yields the magnitude of k2 (see Eq. [26]).
Finally on plotting ln(k2K~p) against 1/T the
activation energy E~)t may be evaluated. The
absolute value Ksp need not be known in this
evaluation, only its temperature dependence.
The calculated values of n and m are listed
in Table I. Considering the detailed procedure
-
Journal of Colloid and Interface Science, Vol. 102, No. 1, November 1984
274
VAN STRATEN AND DE BRUYN
b
oo
a
-3
f(~
c
,
d
)
-2
-1-
-0.1
-
.5
-1.0
Log( 1-- ~ ( t ) )
FIG. 11. Illustrative plots of growth rates, f ( a ) = log X ~(/)-2/3. d c q d t versus log normalized aluminate
concentration, log(1 - ct(t)) at different temperatures and different growth phases. (a) Gibbsite: 75°C,
pOH 3.35. (b) Bayerite: 50°C, pOH 3.45. (c) Bayerite: 50°C, pOH 3.65. (d) Bayerite: 75°C, pOH 3.85.
(e) Pseudoboehmite: 50°C, pOH 4.25. (f) Pseudoboehmite: 75°C, pOH 4.25. O n (e) and (f) the x-axis is
plotted the function log(1 - a*(t)), see text.
involved in the evaluation of the activation concentration at all the temperatures invesenergy (see Eq. [25]) this, growth parameter tigated. As the nature of the growth unit
is known less accurately than the reaction cannot be directly established from our exorders. In the temperature range, 50-75°C, periments this second-order dependence may
where m is roughly equal to n, the activation also be interpreted as a first-order dependence
energy for growth of gibbsite and bayerite is on the concentration of a dimer (for example,
estimated to equal 68 _+ 10 kJ/mole. This AIz(OH) 7). Except for measurements at room
value corresponds reasonably well with those temperature the reaction order in [H ÷] is
estimates for gibbsite growth based on seed seen to be somewhat higher than two. This
experiments (17, 21) where also a second- observation is in general agreement with the
order dependence on supersaturation was assumed dependence of q and probably also
observed. Misra and White (17) quote a ko, on pH. A general second-order depenvalue of 60 kJ/mole and King (21) 53 kJ/ dence of the growth of bayerite and gibbsite
mole for ~.Cg)
on the supersaturation H is therefore not
~t.,act o
For bayerite and for gibbsite as growth excluded by this investigation.
Once the order m has been established the
phase the data of Table I clearly establish a
second-order dependence on the aluminate available surface area A can be determined
Journal of Colloid and InterfaceScience, Vol. 102, No. 1. November 1984
PRECIPITATION FROM SUPERSATURATED ALUMINATESOLUTIONS, II
from ECl. [21]. The dependence of A on a
may be expressed as
A(t) = constant a(t) z
[27]
where z may be evaluated by plotting log[(1
- a) - m . da/dt] against log a. Note that in
ECl. [23] we have assumed z = 2/3. In the
experiments performed at 50°C only bayerite
is the growth phase at low supersaturation
(see Fig. 5), the available surface area may
then be calculated by taking m = 2 and the
exponent z by plotting log[(1 - a)-2(da/dt)]
against log a. This analysis shows that Eq.
[27] is a good approximation and yields the
values 0.8 (pOH 3.85) and 0.7 (pOH 3.45).
Although the calculated range of z values are
slightly higher than the value 2/3 (Eq. [23])
this finding may be due to complications, for
example, secondary nucleation, introduced
during the growth process. Considering, however, the complex nature of the precipitation
process and the accuracy attainable by the
experimental techniques, we feel justified to
conclude that for this system (bayerite growth)
the relaxation experiments at different temperatures and pOH values are satisfactorily
accounted for by an expression for the growth
rate which is proportional to the available
surface area and the square of the supersaturation.
As can be seen in Table I there exists a
strong correlation between the empirical II
dependence for growth (n) and nucleation
(p). We believe it reasonable to expect both
the rate of nucleation and of the growth of
bayerite to be controlled by the formation of
two-dimensional nuclei. This would imply
that both rates will be largely determined by
the factor e -AGe(2D)/RT although significant
differences may be noted in the preexponential factors.
An analysis of the growth rate of pseudoboehmite by the same procedure used in the
analysis of bayerite growth data shows the
exponent m to increase strongly with decreasing aluminate concentration. This observation need not be in variance with a
275
surface nucleation growth mechanism because experiment shows pseudoboehmite to
grow at substantially lower supersaturations
than bayerite and therefore under conditions
where the theory does predict a steep rise in
m. Direct proof of the applicability of this
mechanism is, however, not available. We
have already shown that the experimental
growth data for pseudoboehmite fit the empirical relation (see curves e and f, Fig. 11)
= k"(T)a(n
-
1) m'
[28]
where, (II - 1) is the relative supersaturation,
proportional to the concentration difference,
CA~(t)- cAa(equil), and m' is a constant, approximately equal to unity (see Table I).
Values for n' describing the dependence of
the growth rate on [H+]), are also listed in
Table I. The observed functional dependence
of/~ on the relative supersaturation (II - 1)
instead of the supersaturation, II (ECl. [21])
is not too surprising because the relatively
low supersaturation of the solution with
respect to pseudoboehmite combined with
the high solubility (pKsp (pseudoboehmite)
~. -1.1), clearly suggest that the equilibrium
concentration, CAl(equil), is not negligible
compared to CAl(t). We note, furthermore,
that with m' = 1, Ecl. [28] has the appropriate
form for a kinetic process controlled by
volume diffusion. A very rough calculation
of the growth rates to be expected in our
system assuming the kinetics to be diffusioncontrolled, yields, however, rates much larger
than those observed experimentally. We believe therefore that this interpretation of ECl.
[28] may be discarded but are not able to
offer a more acceptable alternative. In conclusion we should remark that this empirical
relation has also been reported to describe
crystal growth rates of a number of simple
salts from supersaturated solutions (22).
CONCLUSION
This study confirms the precipitation sequence observed at 25°C (1) in supersaturated
Journal of Colloid and Interface Science, Vol. t02, No. 1, November 1984
276
VAN STRATEN AND DE BRUYN
cleation of bayerite may also be described by
an empirical relation between relaxation time
and supersaturation featuring a power law
amorphous -~ pseudoboehmite --~
dependence on supersaturation and yields an
activation energy Frt2)
~act ~ 95 kJ mole -l. The
bayerite ~ gibbsite.
difference in the two estimated activation
Regardless of the temperature the least-stable energies may be shown to be largely deterphase is found to precipitate first as predicted mined by the standard enthalpy of the preby the Ostwald rule of stages. The amorphous cipitation reaction.
The growth rate of bayerite is shown to be
phase forms rapidly as is evidenced by the
pseudoequilibrium titration curves at fast proportional to the available surface area and
titration speeds. Its estimated solubility prod- the square of the supersaturation. The actiuct does not change significantly with tem- vation energy is estimated to have the same
perature; pKsp --- -log aAl~OH~/aorI- ~ --1.9. magnitude (60-80 kJ/mole) as that observed
The formation rate of the other phases is from gibbsite seed experiments. The growth
measurable and may be interpreted in terms of pseudoboehmite cannot be described by
constant power dependence on supersaturaof nucleation and growth mechanisms.
tion.
It is approximately proportional to surGrowth of bayerite is retarded by small
face
area
and the relative supersaturation (17
amounts of pseudoboehmite at all tempera1).
tures and from an analysis of the relaxation
Finally, we note that the transition from
time curves, a solubility for pseudoboehmite
(pKsp ~ -1.3 to -1.2) which is nearly in- bayerite to gibbsite could not be detected by
dependent of temperature has been evaluated. observable discontinuities or inflections in
Bayerite forms in large amounts at room relaxation times or growth curves. The
temperature. At higher temperatures the pre- smooth transition behavior indicates that the
cipitation rates of pseudoboehmite (high pOH formation of these two crystalline phases
values) and gibbsite (at low pOH values) proceeds by identical mechanisms.
increase faster than that of bayerite (with the
result that the latter phase becomes less domACKNOWLEDGMENT
inant and may even disappear completely.
The authors wish to thank J. Suurrnond for his
Analysis of the experimental relaxation
assistance with the electron-microscopy study of the
times indicates that the favored formation of precipitation products.
pseudoboehmite over bayerite at high pOH
values is related to its lower interfacial tension
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